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Factor analysis is a mathematical tool which can be used to examine a wide range of data sets. It has been used in disciplines as diverse as chemistry, sociology, economics, psychology and the analysis of the performance of race horses. This tutorial is designed to provide a basic understanding of the principles underlying factor analysis. The focus of the tutorial is the analysis of a 'factor space' or 'data space'. It was written to introduce the undergraduate chemistry major to the basic concept of a 'data space' and to demonstrate how factor analysis can be used to study a 'data space'. As an aid to conceptualization a geometric approach is used wherever possible and the actual linear algebra involved is illustrated.

Factor analysis requires a set of data points in matrix form; following the terminology used by Malinowski and Howry[1] , the terms 'row designee' and 'column designee' will be used to refer to the row and column identifiers of the matrix. This terminology is used because of the very wide range of data matrix types that may be analyzed by factor analysis. To be factor analyzable the data must be bi-linear; this means that the row entities and the column entities must be independent of each other.